In the phrase homo est albus, both terms suppose the same thing, and it is denoted by the whole proposition that it is the case that the same thing is both a man and white: “denotatur in tali propositione, quod illud, pro quo subiectum supponit, sit illud, pro quo praedicatum supponi” (Exp. in Porph. I, 72).
Likewise, denotari is used to indicate what is demonstrated to be the case by the conclusion of a syllogism: “propter quam ita est a parte rei sicut denotatur esse per conclusionem demonstrationis” (Summa logicae III, 2, 23; see also Moody 1935: sect. 6.3).15
The repeated use of the passive form suggests that a proposition does not denote a state of affairs: rather, by means of a proposition a state of affairs is denoted. It is, then, open to discussion whether denotatio is a relationship between a proposition and what is the case, or between a proposition and what is understood to be the case (see Marmo 1984). Through a proposition something is denoted, even if that something supposes nothing (Summa logicae I, 72).
Be that as it may, considering that (i) the suppositio is a extensional category, and the word “denotation” occurs so frequently in conjunction with the mention of the supposition’ and that (ii) in all probability the proposition does not necessarily denote its truth value, but at least denotes to someone that something is or is not the case,16 we are led to suppose that Ockham’s example may have inspired some later thinkers to use the term denotatio in extensional contexts.
Thanks to the radical shift in meaning of the verb significare between Bacon and Ockham, at this point the term denotare is ready to be considered in an extensional perspective.
It is curious to observe how, if we consider Bacon and Ockham, this terminological revolution first affected the term significatio (involving denotatio almost exclusively as a side effect). But, from the time of Boethius on, the term significatio had found itself so tied in with the concept of “meaning” that it had been able to hold out, so to speak, more courageously against the incursions of the extensionalist point of view. Moreover, in centuries to come, we will continue to encounter significatio, once more used in an intensional sense (see, for example, Locke). Truth-conditional semantics on the other hand was more successful in appropriating the more semantically ambiguous term denotatio.
The cognitivist tradition on the other hand did not follow the lead of using the term “denotation” in relation with meaning.17 Be that as it may, after Mill we find the term “denotation” used more and more in reference to extension.
9.11. After Ockham
Do we have any reason to believe that Mill borrowed the idea of using denotatio as a technical term from Ockham?
There are in fact several reasons to suspect that Mill elaborated his System of Logic with reference to the Ockhamist tradition.
(i) Though he paid considerable attention to the intensional aspects of language, Mill formulated a theory of the denotation of terms in which he makes an affirmation similar to that expressed in Ockham’s theory of supposition: “a name can only be said to stand for, or to be a name of, the things of which it can be predicated” (Mill [1898]1843: II, v).
(ii) Mill borrows from the Schoolmen (and he is the first to admit it—in II, v) the term “connotation” and, in distinguishing between connotative and nonconnotative terms, he states that the latter are defined as “absolute” terms. Gargani (1971: 95) traces back this terminology back to Ockham’s distinction between connotative and absolute terms.
(iii) Mill uses signify in line with the Ockhamist tradition, at least as far as the first meaning assigned to it by the medieval philosopher goes. “A non-connotative term is one which signifies a subject only or an attribute only. A connotative term is one which denotes a subject, and implies an attribute” (II, v). Since the denotative function (in Mill’s scheme of things) is performed in the first place by nonconnotative terms, it is clear that for Mill “to signify” and “to denote” are one and he same. See also: “the name … is said to signify the subjects directly, the attributes indirectly; it denotes the subjects and implies, or involves, or as we shall say henceforth, connotes the attributes … The only names of objects which connote nothing are proper names, and these have, strictly speaking, no signification” (II, v).
(iv) Mill probably opts for “denote” as a more technical and less prejudicial term than “signify,” on account of its etymological opposition to “connote.”
Nevertheless, we have seen that Ockham did not encourage the extensional use of denotare but at most influenced it. Where, in the history of the natural evolution of the term, are we to find the missing link?
The place to look is probably Hobbes’s De corpore I, better known as Computatio sive logica.
It is a matter of general agreement that Hobbes was fundamentally influenced by Ockham, as Mill was by Hobbes. Mill in fact begins his discussion of proper names with an in-depth review of Hobbes’s opinions.
We must, however, note that Hobbes does indeed follow Ockham as far as the theory of universals and propositions is concerned, but at the same time he develops a different theory of signification. For Hobbes in fact there is a clear-cut distinction between signifying (expressing the speaker’s opinions, that is, during an act of communication) and naming (in the classic sense of appellare or supponere, on which see Hungerland and Vick 1981).
Mill ([1898]1843: II, 1) recognizes that for Hobbes names are above all the names of the ideas we have about things, but at the same time he finds in Hobbes proof supportive of the decision that “names, therefore, shall always be spoken of in this work as the names of things themselves,” and the contention that “all names are names of something, real or imaginary … A general name is familiarly defined, a name which is capable of being truly affirmed, in the same sense, of each of an indefinite number of things.” In these passages Mill is close to Hobbes, with the marginal difference that he dubs “general” the names that Hobbes on the other hand dubs “universal.”
However, as we have noted, Mill uses “signify,” not in the Hobbesian sense, but in that of Ockham, and, in place of the notion of “signifying” used by Hobbes, he prefers to employ “connote.” Being deeply interested in connotation, and not realizing that his idea of “connotation” is not all that far away from Hobbes’s “signification,” Mill is convinced that Hobbes privileges nomination (Mill’s “denotation”) over signification (Mill’s “connotation”). In his opinion, Hobbes, like the Nominalists in general, “bestowed little or no attention upon the connotation of words; and sought for their meaning exclusively in what they denote” (II, v).
This decidedly odd reading of Hobbes (as if he were Bertrand Russell) can be explained by the fact that Mill interprets Hobbes as if he were an orthodox follower of Ockham. But, if Mill considers Hobbes an Ockhamist, why does he attribute to him the idea that names denote? Mill claims that Hobbes uses nominare in the place of denotare (II, v), but he had probably observed that, in the De corpore, Hobbes used denotare in four cases at least—five in the English translation of Hobbes’s Latin that Mill probably read, since he cites Hobbes’s work as Computation or Logic.
As for the difference between abstract and concrete names, Hobbes says that “abstractum est quod in re supposita existentem nominis concreti causam denotat, ut ‘esse corpus,’ ‘esse mobile’… et similia … Nomina autem abstracta causam nominis concreti denotant, non ipsam rem” (De corpore I, iii, 3). It should be underscored that for Hobbes abstract names do in fact denote a cause, but this cause is not an entity: it is the criterion that supports the use of an expression (see Gargani 1971: 86 and Hungerland and Vick 1981: 21). Mill reformulates Hobbes’s text as follows: a concrete name is a name that stands for a thing; an abstract name is a name that stands for an attribute of a thing (1843, II, v)—in which “stand for” is Ockham’s “stare pro aliquo.” He adds, furthermore, that his use of words like “concrete” and “abstract” is to be understood as being in keeping with the usage of the Scholastics.
Mill probably extrapolates from this passage in Hobbes the idea that, if abstract names do not denote things, this is instead the case for concrete nouns. For Hobbes in fact “concretum est quod rei alicujus quae existere supponitur nomen est, ideoque quandoque suppositum, quandoque subjectum, graece ypoleimenon appellatur,” and, two lines above, he writes that, in the proposition corpus est mobile, “quandoque rem ipsam cogitamus utroque nomine designatam” (De corpore I, 111,3). Thus, designare makes its appearance in a context in which it is linked on the one hand to the concept of supposition and on the other to that of denotation.
Since concrete names can be proper either to single things or to sets of individuals, we may say that, if there exists a concept of denotation developed by Hobbes, it is still halfway between between Peter of Spain’s suppositio naturalis and his suppositio accidentalis. This is why Hungerland and Vick (1981: 51 et seq.) stress the fact that denotare could not have had for Hobbes the same meaning it has acquired in our contemporary philosophy of language, because it applies, not only to logical proper names, but also to the names of classes and even to nonexistent entities. But Mill does buy into such a perspective, and therefore could have interpreted Hobbes’s denotare
